Circle Tangent to Line

Date: 04/19/2001 at 17:25:36
From: Lewis
Subject: Given 2 points and tangent, determine circle

I've had trouble finding the circle that passes through two given 
points and is tangent to a line. Knowing where the circle touches the 
tangent has stumped me. I've drawn the perpendicular bisector between 
the points and the perpendicular from the tangent, but stop there.

Date: 04/19/2001 at 18:25:41
From: Doctor Jaffee
Subject: Re: Given 2 points and tangent, determine circle

Hi Lewis,

You're almost there. The perpendicular bisector that you constructed 
between the two given points must pass through the center of the 
circle. Furthermore, the length of the segment that connects the 
tangent line and the perpendicular bisector must equal the length of 
the radius.

So, set the radius of your compass equal to the length of the segment 
that connects the tangent line and the perpendicular bisector, and 
place the point of your compass on one of the given points. Where the 
arc crosses the perpendicular bisector will be the center of your 
circle.

If you need an algebraic solution, you can use an analogous procedure. 
 
I hope this works for you. Let me know if you have any difficulties.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/